Conventionally, reflective projection display devices configured to display images by reflecting ambient light such as sunlight and interior light. An example of such devices is disclosed in Patent Document 1. Patent Document 1 discloses a multilayer color cholesteric liquid crystal display element including a first blue liquid crystal layer, a second green liquid crystal layer, and a third red liquid crystal layer laid in layers sequentially from the component observation side. The multilayer color cholesteric liquid crystal display element further includes green cut filter layers for selectively absorbing light beams having a wavelength of 600 nm or less between the green liquid crystal layer and the red liquid crystal layer. According to the configuration, unnecessary color noises can be removed.